Stitz-Zeager_College_Algebra_e-book

However theorem 1116 pays huge dividends when

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Unformatted text preview: olar Equations 801 Next, as θ runs from π to π , we see that r increases from 2 to 4. Picking up where we left 2 off, we gradually pull the graph away from the origin until we reach the negative x-axis. y r θ runs from 6 π 2 to π x 4 2 π 2 π 3π 2 2π θ π Over the interval π , 32 , we see that r increases from 4 to 6. On the xy -plane, the curve sweeps out away from the origin as it travels from the negative x-axis to the negative y -axis. y r 6 x 4 2 π 2 π 3π 2 2π θ θ runs from π to 3π 2 π Finally, as θ takes on values from 32 to 2π , r decreases from 6 back to 4. The graph on the xy -plane pulls in from the negative y -axis to finish where we started. y r 6 x 4 2 π 2 π 3π 2 2π θ runs from θ 3π 2 to 2π We leave it to the reader to verify that plotting points corresponding to values of θ outside the interval [0, 2π ] results in retracing portions of the curve, so we are finished. 802 Applications of Trigonometry y r 2 6 −4 4 4 x 2 π π 2 2π 3π 2 −6 θ r = 4 − 2 sin(θ) in the θr...
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